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Electromagnetic induction
Electromagnetism 

Electricity · Magnetism 
Lorentz force law • emf • Electromagnetic induction • Faraday’s law • Lenz's law • Displacement current • Maxwell's equations • EM field • Electromagnetic radiation • Liénard–Wiechert potential • Maxwell tensor • Eddy current

Electromagnetic induction is where a voltage or current is produced in a conductor by a changing magnetic flux. It may happen when a magnet is moved in a solenoid, thus changing the magnetic flux.
Magnetic flux
When a coiled wire is introduced near a magnet, the magnetic lines of force pass through the coil. This causes the magnetic flux to change. Magnetic flux is represented by the symbol [math]{\Phi}[/math], therefore we can say that [math]{\Phi}[/math] = BAcos(a) and the resulting unit will be [math]Tm^2[/math], where T is the unit for magnetic field and [math]m^2[/math] is the unit for area.
The changing magnetic flux generates an electromotive force (EMF). This force moves free electrons in a certain way, which constitute a current.
Faraday's law
Michael Faraday found that an electromotive force is generated when there is a change in magnetic flux in a conductor.
His laws state that:
[math] \mathcal{E} = {{d\Phi} \over dt}[/math]
where,
[math]\mathcal{E}[/math] is the electromotive force, measured in volts;
[math]{d\Phi}[/math] is the change in magnetic flux, measured in webers;
[math]dt[/math] is the change in time, measured in seconds.
In the case of a solenoid:
[math] \mathcal{E} = {N{d\Phi} \over dt}[/math]
where,
N is the number of loops in the solenoid.
Lenz's law
The negative sign in both equation above is a result of Lenz's law, named after Heinrich Lenz. His law states that the electromotive force (EMF) produces a current that opposes the motion of the changing magnetic flux.
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